Question: Solve for $x$ and $y$ using substitution. ${-4x+5y = 1}$ ${y = -x+11}$
Solution: Since $y$ has already been solved for, substitute $-x+11$ for $y$ in the first equation. ${-4x + 5}{(-x+11)}{= 1}$ Simplify and solve for $x$ $-4x-5x + 55 = 1$ $-9x+55 = 1$ $-9x+55{-55} = 1{-55}$ $-9x = -54$ $\dfrac{-9x}{{-9}} = \dfrac{-54}{{-9}}$ ${x = 6}$ Now that you know ${x = 6}$ , plug it back into $\thinspace {y = -x+11}\thinspace$ to find $y$ ${y = -}{(6)}{ + 11}$ $y = -6 + 11$ $y = 5$ You can also plug ${x = 6}$ into $\thinspace {-4x+5y = 1}\thinspace$ and get the same answer for $y$ : ${-4}{(6)}{ + 5y = 1}$ ${y = 5}$